Question
Download Solution PDFFind the length of the latus rectum of the parabola y2 = - 12x ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
The following are the properties of a parabola of the form: y2 = - 4ax where a > 0
- Focus is given by (- a, 0)
- Vertex is given by (0, 0)
- Equation of directrix is given by: x = a
- Equation of axis is given by: y = 0
- Length of latus rectum is given by: 4a
- Equation of latus rectum is given by: x = - a
CALCULATION:
Given: Equation of parabola is y2 = - 12x
The given equation can be re-written as: y2 = - 4 ⋅ 3 ⋅ x---------(1)
Now by comparing the equation (1), with y2 = - 4ax we get
⇒ a = 3
As we know that, the length of latus rectum of a parabola is given by: 4a
So, length of latus rectum of the given parabola is: 4 ⋅ 3 = 12 units
Hence, option B is the correct answer.
Last updated on Jun 30, 2025
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